Partially Loaded Rectangular Plate

This Demonstration shows an approximate method for determining the deflection of a rectangular plate, freely supported at the boundary (so that the momentum on the boundary is zero). With regard to the material, the calculation is based on Young's modulus and the Poisson ratio. To understand the problem more easily, the graphic shows the load as a cuboid whose height corresponds to a unit load if the cuboid is made of iron.
The governing differential equation is .

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DETAILS

Consider the differential equation for the problem,
,
and assume that (the deviation of the plate) is
,
where the are constant. Substituting for in the first equation gives
.
Then
,
and finally,
.
Reference: S. Timoshenko, Theory of Plates and Shells, New York: McGraw–Hill, 1959.
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